A method of this type is disclosed in U.S. Pat. No. 3,455,617. For the axial mounting of a bearing in a housing, a flange with a sleeve-shaped extension is provided which is pressed against an outer ring of the bearing, which is thereafter supported in the housing. The flange is accordingly bolted to the housing. In order to compensate for manufacturing tolerances, the front face of the sleeve-shaped extension is provided with an annular projection which has an axially pointed longitudinal section. The projection is plastically deformed, i.e. coined, when pressed against the outer ring, until the flange attains its axial position by contact against the housing. After the plastic deformation of the material at the tip of the projection, the material in the remaining areas undergoes elastic restoring forces, so that after this procedure a typical axial attachment with prestress is attained. The geometric form of the projection and the use of the area of plastic deformation by compression of the material greatly limits the range of manufacturing tolerances which this method can accommodate. The material of the annular peaked projection undergoes, as is evident from the drawing of the cited reference, relatively short axial strain displacement up to the compression limit, beyond which further deformation is in practice no longer possible. Furthermore, the reaction force progressively increases because of the geometric shape of the projection so that the prestress produced thereby is directly dependent on the tolerance range being compensated for. This is unacceptable for the application of the rolling bearing. A further disadvantage is the relatively small surface area of contact between the projection and the outer ring, which for alternative applications leads to deformation of the attached machine parts. In contrast to the type of attachment disclosed in the cited reference, the known process can also be used for adjustment of the relative positions of machine parts, wherein the deformable projection determines the mutual distance between the machine parts.